The population triples ( P × 3 ) every ten minutes...

So if ten minutes is reached there will be 1,200 bacteria.

Edited - missed the question
** The units for time should be in minutes.

P = 400 × 3^(t/10)

at t = 0 ; P = 400
at t = 10 ; P = 1,200

When P = 600
600 = 400 × 3^(t/10)
6/4 = 3^(t/10)
Log(3/2) = Log(3^(t/10))
power rule
Log(3/2) = (t/10) Log(3)
10 × Log(3/2)/Log(3) = t

3.69 minutes the population will be at 600 bacteria
Unites for time are in minutes.

6 0

3 years ago

In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour

Lesechka [4]

Answer:

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=54$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=21$ represent the sample standard deviation

n=16 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.90 or 90%, the value of $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$